Relative proper motions are determined for stars brighter than B~=17mag in a 1.5{deg}x1.5{deg} field centered on the globular cluster NGC 362. Proper motions and membership probabilities are tabulated for 488 stars within 10.2' of the cluster center. 14 astrographic plates with epoch differences up to 92 years were completely scanned, and each detectable object was stored. Proper motions were computed with an iterative central-overlap technique. A modal proper motion accuracy of 0.9 milliarcsec/year (mas/a) was achieved. NGC 362 appears projected onto the Small Magellanic Cloud (SMC), allowing to measure the proper motion of the cluster relative to extragalactic background stars. SMC stars were identified by position, proper motion and colour; the mean proper motion of these SMC candidates agrees well with the proper motions of SMC members known from the literature. The proper motion of NGC 362 relative to the SMC is +3.5+/-0.8mas/a in right ascension and -2.6+/-0.8mas/a in declination. For reasonable assumptions on the absolute proper motion of the SMC, the absolute proper motion and space motion of NGC 362 are computed. NGC 362 exhibits a highly eccentric orbit, typical for a member of the halo subgroup of the galactic globular cluster system. The perigalactic distance of NGC 362 is very small (<~1kpc), which raises the interesting question of how the cluster can survive the many passages near the galactic bulge over its lifetime.